-LRB- CNN -RRB- -- European leaders are meeting in Brussels Thursday to discuss further sanctions against Russia .

So far the EU has imposed financial and visa restrictions against 21 carefully selected Russian and Ukrainian officials -- but avoided anyone from President Vladimir Putin 's inner circle and stayed clear of any large-scale economic sanctions .

The EU and U.S. have condemned Russian annexation of Crimea as illegal and stepped up their rhetoric towards the Kremlin , but whether they are willing to put more economic pressure on Russia is unclear .

The leaders of Europe 's biggest economies are likely to be cautious .

Here 's why .

How important is Russia 's economy ?

Russia is the eight biggest economy in the world , with GDP of more than $ 2 trillion . But its economy -- which is heavily reliant on commodities , particularly oil and gas , was growing just 1.3 % last year compared to 2012 , one of the sharpest slowdowns in the emerging markets .

With the Ukraine crisis taking its toll , Russia 's economy may not grow at all in 2014 , some analysts have warned .

Hopes Russia would be one of the decade 's powerhouse economies may have faded , but its close links with the European Union have not .

Would sanctions hit Europe back ?

The EU is Russia 's largest trading partner , and there are deep economic links between the two . Almost half of Russia 's exports -- $ 292 billion worth -- end up in EU countries . 15 % of Russia 's GDP comes directly from the country 's exports to EU . Russia , in turn , is the third biggest trading partner for the EU , with $ 169 billion in imports .

But the eurozone itself has only just emerged from its own crisis , and is wary of cutting ties with such a powerful economic partner . Its reliance on gas out of Russia would also feed caution .

Robert Pape , political science professor at University of Chicago with expertise in security studies , says the sanctions would hurt both sides . `` Between great powers , leverage is a two-way street , Russia can squeeze us almost as effectively as we can squeeze them , '' Pape wrote for CNN .

While steps that would push the price of oil down for a sustained period would really bite , these would be hitting right back . Energy supplies remain vitally important for the European Union , to which Russia supplies a third of EU 's natural gas . Germany , the eurozone 's biggest economy , imports around 40 % of its gas from Russia .

What is Russia 's economic relationship with the U.S ?

The economic relationship between Russia and the U.S. is more unbalanced . Russia is the 20th largest trading partner for the U.S. , with $ 27 billion worth of trade exported across the Atlantic . On the flip-side , the U.S. is Russia 's fifth largest partner , with just $ 11 billion worth of trade .

According to Russian Foundation chair David Clark , trade is a `` relatively unimportant '' component of relations . Energy links are also weakening as the U.S. looks to shale gas for its energy supplies and heads towards self-sufficiency .

Clark told CNN the U.S. could get greater leverage over Russia from financial sanctions aimed at the country 's banking system and stability of the ruble . Measures targeted at named individuals , similar to those contained in the Magnitsky Act , could also be effective . `` Russia 's angry response to the act shows that it works , '' Clark said .

But again , the financial links between Russia and the west would mean huge losses for European banks which have lent billions to Russia .

While the EU and U.S. adopted sanctions against 28 individuals , Clark said these `` have little more than nuisance value and would have to be dramatically expanded to have a real impact . ''

`` Travel bans and asset freezes aimed at all members of the Duma and Federation Council who voted to annex Crimea would be a start , '' Clark said .

Targeting the money men who handle the finances and assets -LRB- often illicit -RRB- of top tier politicians would really hurt , he added . And the names of these individuals are quite well known .

But again , the financial links between Russia and the west would mean huge losses for European banks which have lent billions to Russia .

Are there other options ?

The EU has a wide range of legal options here . Its economic significance means sanctions can be very powerful tool . Export and import bans or restrictions that apply to specific products such as oil or diamonds , flights restrictions or investment freezes have been successful in the past .

`` Restricting access to foreign capital and the international banking system could prove very damaging indeed because Russia 's economy is stagnating and it needs inward investment , '' Clark said .

But experience shows that economic sanctions rarely work in the pursuit of non-economic goals . `` Imposing economic sanctions on a state is similar to backing an angry dog into a corner -- in most cases , the dog will become more vicious , and more defensive , '' Pape said .

At the end , targeting Russia 's national pride may prove more useful .

`` A decision by a large group of countries to boycott the 2018 Football World Cup in Russia would probably hurt Russian prestige rather more , especially if FIFA had to move the event to another country , '' David Clark said .

Read more :

Why annexing Crimea may prove costly for Russia
West 's sanctions on Russia : Are they just for show ?
Is Russia 's annexation of Crimea opportune or opportunistic ?

CNN 's Irene Chapple and Mark Thompson contributed to this report .

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European leaders are discussing further economic sanctions against Russia

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The United States and Europe targeted 28 Russian and Ukrainian officials

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Tight economic links between Russia and the EU could mean sanctions hurt both sides